Act I – When Cats Are Maddened by the Midnight Dance

After the overture, the cats gather on stage and describe the Jellicle tribe and its purpose ("Jellicle Songs for Jellicle Cats"). The cats (who break the fourth wall throughout the show) then notice that they are being watched by a human audience, and proceed to explain how the different cats of the tribe are named ("The Naming of Cats"). This is followed by a ballet solo performed by Victoria to signal the beginning of the Jellicle Ball ("The Invitation to the Jellicle Ball"). At this moment, Munkustrap, the show's main narrator, explains that tonight the Jellicle patriarch Old Deuteronomy will make an appearance and choose one of the cats to be reborn into a new life on the Heaviside Layer.

The first contender Munkustrap introduces is Jennyanydots ("The Old Gumbie Cat"), a large tabby cat who lazes around all day, but come nighttime, she becomes active, teaching mice and cockroaches various activities to curb their naturally destructive habits. Just as Jennyanydots finishes her song, the music changes suddenly and Rum Tum Tugger makes his extravagant entrance in front of the tribe ("The Rum Tum Tugger"). He is very fickle and unappeasable, "for he will do as he do do, and there's no doing anything about it".

Then, as Rum Tum Tugger's song fades, a shabby old grey cat stumbles out wanting to be reconciled; it is Grizabella. All the cats back away from her in fear and disgust and explain her unfortunate state ("Grizabella: The Glamour Cat"). Grizabella leaves and the music changes to a cheerful upbeat number as Bustopher Jones, a fat cat in "a coat of fastidious black", is brought to the stage ("Bustopher Jones: The Cat About Town"). Bustopher Jones is among the elite of the cats, and visits prestigious gentlemen's clubs. Suddenly, a loud crash startles the tribe and the cats run offstage in fright. Hushed giggling sounds signal the entrance of Mungojerrie and Rumpleteazer, a pair of near-identical cats. They are mischievous petty burglars who enjoy causing trouble around their human neighbourhood ("Mungojerrie and Rumpleteazer"). After they finish, they are caught off-guard and confronted by the rest of the cats.

Finally, the Jellicle patriarch, Old Deuteronomy, arrives before the tribe ("Old Deuteronomy"). He is a wise old cat who "has lived many lives" and is tasked with choosing which Jellicle will go to the Heaviside Layer every year. The cats put on a play for Old Deuteronomy ("The Awefull Battle of the Pekes and the Pollicles"), telling a story about two dog tribes clashing in the street and subsequently being scared away by the Great Rumpus Cat. A sombre moral from Old Deuteronomy is interrupted by a second loud crash, presumably from Macavity, which sends the alarmed cats scurrying. After a quick patrol for Macavity, Old Deuteronomy deems it a false alarm and summons the cats back as the main celebration begins ("The Jellicle Ball"), in which the cats sing and display their "Terpsichorean powers".

During the Ball, Grizabella reappears and is once again shunned by the other cats ("Grizabella: The Glamour Cat (Reprise)") while Old Deuteronomy looks on sadly. She tries to dance along, but her age and decrepit condition prevent her from doing so ("Memory (Prelude)").

Act II – Why Will the Summer Day Delay – When Will Time Flow Away?

After the Jellicle Ball, Old Deuteronomy contemplates "what happiness is", referring to Grizabella. However, the cats do not understand him, so he has Jemima (also known as Sillabub), the youngest of all Jellicles, sing it in simpler terms ("The Moments of Happiness"). Gus – short for Asparagus – shuffles forward as the next cat to be introduced ("Gus: The Theatre Cat"). He was once a famous actor but is now old and "suffers from palsy which makes his paws shake". He is accompanied by Jellylorum, his caretaker, who tells of his exploits. Gus then remembers how he once played the infamous pirate captain, Growltiger a.k.a. the Terror of the Thames ("Growltiger's Last Stand"). Gus tells the story about the pirate captain's romance with Lady Griddlebone, and how Growltiger was overtaken by the Siamese and forced to walk the plank to his death.

Back in the present, after Gus exits, Skimbleshanks is seen sleeping in the corner ("Skimbleshanks: The Railway Cat"). He is the cat who is unofficially in charge of the night train to Glasgow. Skimbleshanks is considered vital to the rail operations, as without him "the train can't start". Within his song, a whole steam train engine is assembled out of objects in the junkyard.

With a third crash and an evil laugh, the "most wanted" cat Macavity appears. He is the so-called "Napoleon of Crime" who always manages to evade the authorities. Macavity's henchmen capture Old Deuteronomy and take off with the patriarch in tow. As Munkustrap and his troop give chase, Demeter and Bombalurina explain what they know about Macavity ("Macavity: The Mystery Cat"). When they are finished, Macavity returns disguised as Old Deuteronomy, but his cover is blown by Demeter and he ends up in a fight with Munkustrap and Alonzo. Macavity holds his own for a time, but as the rest of the tribe begin to gang up and surround him, he shorts out the stage lights and escapes in the resulting confusion.

After the fight, Rum Tum Tugger calls upon the magician Mr. Mistoffelees for help ("Magical Mr. Mistoffelees"). Known as the "original conjuring cat", Mr. Mistoffelees can perform feats of magic that no other cat can do. He displays his magical powers in a dance solo and uses them to restore the lights and bring back Old Deuteronomy. Now, the Jellicle Choice can be made.

Before Old Deuteronomy can announce his decision, Grizabella returns to the junkyard and he allows her to address the gathering. Her faded appearance and lonely disposition have little effect on her song ("Memory"). With acceptance and encouragement from Jemima and Victoria, her appeal succeeds and she is chosen to be the one to go to the Heaviside Layer and be reborn into a new Jellicle life ("The Journey to the Heaviside Layer"). A tyre rises from the piles of junk, carrying Grizabella and Old Deuteronomy partway towards the sky; Grizabella then completes the journey on her own. Finally, Old Deuteronomy gives an address to the audience, closing the show ("The Ad-dressing of Cats").